Record the 1671st column, the first since the 1620th (#167) (#854)

The half of #167 the benchmark itself could not supply. #850 added EvalTrig and
EvalTrigPrecise and stopped the allocation figure being discarded, and the
Kernel Benchmark has now run on master with both, so the numbers come from a
GitHub runner rather than a contributor's machine.

Trigonometry at five hundred digits is 43.3 ms against 1.3 ms at the default
hundred.

Allocation gets a table of its own rather than doubling the width of the main
one. EvalEasy allocating nothing is the proof of the caching note above it
rather than a further argument for it.

Author: Rafael-SOWNet

Sources/AngouriMath/Docs/WhatsNew/version_performance_control.md

@@ -21,7 +21,7 @@ on a path that does not exist and had not run since 2026-01-02 -- ninety-eight m
 requests went unmeasured. Fixed in
 [#775](https://github.com/asc-community/AngouriMath/issues/775).
 
-**Allocation is reported alongside the timings** from the column after the 1620th. The
+**Allocation is reported alongside the timings** from the 1671st column on. The
 benchmark class has carried `[MemoryDiagnoser]` all along, so the figure was measured on every
 run and then discarded, because the reporting code asked for `Mean`, `Error` and `StdDev` and
 nothing else. Asked for by [#167](https://github.com/asc-community/AngouriMath/issues/167).
@@ -47,22 +47,57 @@ take a millisecond in total, while a thousand evaluations of freshly built nodes
 The row is kept as it is so the column history stays comparable, and the two trigonometric
 benchmarks build their expression afresh on every call for exactly this reason.
 
-|          Method |         [331st](https://github.com/asc-community/AngouriMath/commit/10e6e5a90e7270336b68dc5fd6aa36f3e0e65d2b) |          [380th](https://github.com/asc-community/AngouriMath/commit/73ae36488ddb863c1d6f35db5ed2f5dcf1484a26) |     [391st](https://github.com/asc-community/AngouriMath/commit/c7e08e6936bfdc2373377bec81ffd160e406244f)      |         [410th](https://github.com/asc-community/AngouriMath/commit/20814936bc740a9f410af4a4368e9895eab7aaf7) |           [483rd](https://github.com/asc-community/AngouriMath/commit/355963dcdf0ff9da568e9f1144ad2b7b68c19584) |         [520th](https://github.com/asc-community/AngouriMath/commit/70aa71acb73307c9f7df0aac006faae31b06058c) |         [690th](https://github.com/asc-community/AngouriMath/commit/5cc894939cb3657f0aa7ef5a25fd55011058929f) |         [826th](https://github.com/asc-community/AngouriMath/commit/87e33ec3590a95dd4ec59ff5c1f77064a64196d1) |         [914th](https://github.com/asc-community/AngouriMath/commit/6134338df083a908369b6bcfb69e70a4269ec51b) |         [920th](https://github.com/asc-community/AngouriMath/commit/501a0a3a9b2e07cddf92c4446b73ad6e2748253a) |        [1034th](https://github.com/asc-community/AngouriMath/commit/a3f48b47795b2dc2b3435152989a6e15639a65b4) |        [1066th](https://github.com/asc-community/AngouriMath/commit/a33746651f56a380b6c17913aa844f162f258d8c) |        [1090th](https://github.com/asc-community/AngouriMath/commit/9530c5b04484e98023941f7693bbeb1a3282cee6) |           [1446th](https://github.com/asc-community/AngouriMath/commit/2abb2b537c03977281f3fc2cab1da2c78c36a5f5) | [1620th](https://github.com/asc-community/AngouriMath/commit/e05d71797f53a9ac7dbdad6075cd7302a91036e7) |
-|---------------- |--------------:|---------------:|---------------:|--------------:|----------------:|--------------:|--------------:|--------------:|--------------:|--------------:|--------------:|--------------:|--------------:|-----------------:|--------------:|
-|       ParseEasy |        28,599 |         73,669 |        134,120 |        44,328 |          54,675 |        21,722 |        32,212 |        32,138 |        34,702 |        32,199 |        33,008 |        27,483 |        33,043 |        34,664 | 11,760 ns |
-|       ParseHard |        92,037 |        208,710 |        415,440 |       178,760 |         287,865 |       209,853 |       624,769 |       698,094 |     4,272,898 |     3,862,375 |     4,731,275 |     4,051,823 |     5,284,613 |     5,657,058 | 2,617,362 ns |
-|    SimplifyEasy |     6,225,707 |     16,387,374 |     41,081,822 |       397,973 |       2,594,367 |       168,462 |       225,393 |       281,626 |       122,809 |        79,184 |        94,505 |        86,478 |       102,600 |        87,759 | 153,704 ns |
-|    SimplifyHard | 3,245,613,128 |  8,120,319,273 |  9,715,629,251 | 7,477,089,153 |  13,529,147,530 | 3,015,302,746 | 3,162,675,550 | 3,826,831,860 | 4,024,002,060 | 2,633,113,653 | 3,262,112,233 | 4,540,783,876 | 4,639,170,780 | 4,880,264,786 | 2,848,037,261 ns |
-|        Derivate |         5,550 |         39,895 |        161,507 |        50,858 |          56,255 |        37,702 |        46,083 |        86,751 |        68,604 |        41,388 |        58,340 |        48,376 |        54,228 |        60,425 | 26,808 ns |
-|       SolveEasy |       677,259 |      4,066,049 |     33,760,616 |     7,556,902 |     124,888,489 |    38,935,084 |    42,101,926 |    43,102,578 |    43,778,486 |    42,818,770 |    42,230,213 |    35,415,096 |    45,032,006 |    45,587,157 | 21,829,186 ns |
-| SolveEasyMedium |       192,319 |        741,114 |      2,861,751 |       646,063 |         789,993 |       124,082 |       154,729 |       142,744 |       138,836 |        78,712 |       110,144 |        88,021 |       106,430 |       108,175 | 48,368 ns |
-|     SolveMedium |    22,487,990 |    126,650,858 |    690,232,457 |   178,691,349 |     350,752,882 |     2,961,363 |     2,174,299 |     2,108,050 |     2,248,458 |     2,449,733 |     2,996,001 |     2,661,744 |     3,272,498 |     4,409,082 | 783,737 ns |
-| SolveMediumHard |       > 1 h   |       > 1 h    | 12,033,099,074 | 2,754,157,261 |   5,779,298,835 |   240,930,082 |   258,560,720 |   309,944,856 |   346,532,318 |   258,799,676 |   305,404,083 |   354,286,153 |   409,437,694 |   453,280,166 | 124,316,631 ns |
-|       SolveHard |       > 1 h   |       > 1 h    | 21,565,808,100 | 5,636,112,783 | 100,663,275,757 | 1,862,768,773 | 2,532,972,635 | 3,000,655,673 | 3,606,412,386 | 2,425,286,433 | 2,918,112,980 | 3,162,162,893 | 3,353,403,193 | 3,494,150,836 | 1,134,532,585 ns |
-|        EvalEasy |        12,059 |        200,766 |      1,548,901 |       550,676 |       3,354,484 |            34 |            72 |            68 |            84 |            28 |            11 |            11 |            13 |             9 | 2 ns |
-|     CompileEasy |        24,771 |         38,300 |         62,328 |        33,684 |          40,751 |         9,208 |        15,467 |         5,487 |         5,623 |         6,283 |         6,254 |         5,143 |       565,597 |       589,540 | 352,800 ns |
-|     CompileHard |        61,572 |         84,042 |        139,499 |        73,738 |          96,203 |        18,274 |        26,390 |        14,782 |        15,657 |        17,986 |        17,672 |        14,902 |     1,234,995 |     1,321,375 | 595,593 ns |
-|         RunEasy |           138 |            126 |            123 |           117 |             128 |           157 |           170 |           165 |           175 |           167 |           161 |           149 |            48 |            43 | 42 ns |
-|       RunMedium |           833 |            950 |            920 |           844 |             838 |         1,008 |         1,081 |         1,064 |         1,155 |         1,089 |           982 |           875 |           630 |           549 | 318 ns |
-|         RunHard |         1,403 |          1,644 |          1,558 |         1,427 |           1,391 |         1,974 |         2,102 |         2,037 |         2,046 |         2,044 |         1,855 |         1,655 |         1,041 |           928 | 586 ns |
-																													   
+|          Method |         [331st](https://github.com/asc-community/AngouriMath/commit/10e6e5a90e7270336b68dc5fd6aa36f3e0e65d2b) |          [380th](https://github.com/asc-community/AngouriMath/commit/73ae36488ddb863c1d6f35db5ed2f5dcf1484a26) |     [391st](https://github.com/asc-community/AngouriMath/commit/c7e08e6936bfdc2373377bec81ffd160e406244f)      |         [410th](https://github.com/asc-community/AngouriMath/commit/20814936bc740a9f410af4a4368e9895eab7aaf7) |           [483rd](https://github.com/asc-community/AngouriMath/commit/355963dcdf0ff9da568e9f1144ad2b7b68c19584) |         [520th](https://github.com/asc-community/AngouriMath/commit/70aa71acb73307c9f7df0aac006faae31b06058c) |         [690th](https://github.com/asc-community/AngouriMath/commit/5cc894939cb3657f0aa7ef5a25fd55011058929f) |         [826th](https://github.com/asc-community/AngouriMath/commit/87e33ec3590a95dd4ec59ff5c1f77064a64196d1) |         [914th](https://github.com/asc-community/AngouriMath/commit/6134338df083a908369b6bcfb69e70a4269ec51b) |         [920th](https://github.com/asc-community/AngouriMath/commit/501a0a3a9b2e07cddf92c4446b73ad6e2748253a) |        [1034th](https://github.com/asc-community/AngouriMath/commit/a3f48b47795b2dc2b3435152989a6e15639a65b4) |        [1066th](https://github.com/asc-community/AngouriMath/commit/a33746651f56a380b6c17913aa844f162f258d8c) |        [1090th](https://github.com/asc-community/AngouriMath/commit/9530c5b04484e98023941f7693bbeb1a3282cee6) |           [1446th](https://github.com/asc-community/AngouriMath/commit/2abb2b537c03977281f3fc2cab1da2c78c36a5f5) | [1620th](https://github.com/asc-community/AngouriMath/commit/e05d71797f53a9ac7dbdad6075cd7302a91036e7) | [1671st](https://github.com/asc-community/AngouriMath/commit/253b5a8d598a9a1d721b777340bd53ae3be12f99) |
+|---------------- |--------------:|---------------:|---------------:|--------------:|----------------:|--------------:|--------------:|--------------:|--------------:|--------------:|--------------:|--------------:|--------------:|-----------------:|--------------:|--------------:|
+|       ParseEasy |        28,599 |         73,669 |        134,120 |        44,328 |          54,675 |        21,722 |        32,212 |        32,138 |        34,702 |        32,199 |        33,008 |        27,483 |        33,043 |        34,664 | 11,760 ns | 10,857 ns |
+|       ParseHard |        92,037 |        208,710 |        415,440 |       178,760 |         287,865 |       209,853 |       624,769 |       698,094 |     4,272,898 |     3,862,375 |     4,731,275 |     4,051,823 |     5,284,613 |     5,657,058 | 2,617,362 ns | 2,493,337 ns |
+|    SimplifyEasy |     6,225,707 |     16,387,374 |     41,081,822 |       397,973 |       2,594,367 |       168,462 |       225,393 |       281,626 |       122,809 |        79,184 |        94,505 |        86,478 |       102,600 |        87,759 | 153,704 ns | 152,631 ns |
+|    SimplifyHard | 3,245,613,128 |  8,120,319,273 |  9,715,629,251 | 7,477,089,153 |  13,529,147,530 | 3,015,302,746 | 3,162,675,550 | 3,826,831,860 | 4,024,002,060 | 2,633,113,653 | 3,262,112,233 | 4,540,783,876 | 4,639,170,780 | 4,880,264,786 | 2,848,037,261 ns | 2,916,127,943 ns |
+|        Derivate |         5,550 |         39,895 |        161,507 |        50,858 |          56,255 |        37,702 |        46,083 |        86,751 |        68,604 |        41,388 |        58,340 |        48,376 |        54,228 |        60,425 | 26,808 ns | 25,629 ns |
+|       SolveEasy |       677,259 |      4,066,049 |     33,760,616 |     7,556,902 |     124,888,489 |    38,935,084 |    42,101,926 |    43,102,578 |    43,778,486 |    42,818,770 |    42,230,213 |    35,415,096 |    45,032,006 |    45,587,157 | 21,829,186 ns | 21,322,368 ns |
+| SolveEasyMedium |       192,319 |        741,114 |      2,861,751 |       646,063 |         789,993 |       124,082 |       154,729 |       142,744 |       138,836 |        78,712 |       110,144 |        88,021 |       106,430 |       108,175 | 48,368 ns | 48,863 ns |
+|     SolveMedium |    22,487,990 |    126,650,858 |    690,232,457 |   178,691,349 |     350,752,882 |     2,961,363 |     2,174,299 |     2,108,050 |     2,248,458 |     2,449,733 |     2,996,001 |     2,661,744 |     3,272,498 |     4,409,082 | 783,737 ns | 796,814 ns |
+| SolveMediumHard |       > 1 h   |       > 1 h    | 12,033,099,074 | 2,754,157,261 |   5,779,298,835 |   240,930,082 |   258,560,720 |   309,944,856 |   346,532,318 |   258,799,676 |   305,404,083 |   354,286,153 |   409,437,694 |   453,280,166 | 124,316,631 ns | 129,750,583 ns |
+|       SolveHard |       > 1 h   |       > 1 h    | 21,565,808,100 | 5,636,112,783 | 100,663,275,757 | 1,862,768,773 | 2,532,972,635 | 3,000,655,673 | 3,606,412,386 | 2,425,286,433 | 2,918,112,980 | 3,162,162,893 | 3,353,403,193 | 3,494,150,836 | 1,134,532,585 ns | 1,365,230,469 ns |
+|        EvalEasy |        12,059 |        200,766 |      1,548,901 |       550,676 |       3,354,484 |            34 |            72 |            68 |            84 |            28 |            11 |            11 |            13 |             9 | 2 ns | 2 ns |
+|        EvalTrig |             -- |              -- |              -- |            -- |               -- |            -- |            -- |            -- |            -- |            -- |            -- |            -- |            -- |               -- | 1,344,115 ns |
+| EvalTrigPrecise |             -- |              -- |              -- |            -- |               -- |            -- |            -- |            -- |            -- |            -- |            -- |            -- |            -- |               -- | 43,285,515 ns |
+|     CompileEasy |        24,771 |         38,300 |         62,328 |        33,684 |          40,751 |         9,208 |        15,467 |         5,487 |         5,623 |         6,283 |         6,254 |         5,143 |       565,597 |       589,540 | 352,800 ns | 352,449 ns |
+|     CompileHard |        61,572 |         84,042 |        139,499 |        73,738 |          96,203 |        18,274 |        26,390 |        14,782 |        15,657 |        17,986 |        17,672 |        14,902 |     1,234,995 |     1,321,375 | 595,593 ns | 596,664 ns |
+|         RunEasy |           138 |            126 |            123 |           117 |             128 |           157 |           170 |           165 |           175 |           167 |           161 |           149 |            48 |            43 | 42 ns | 42 ns |
+|       RunMedium |           833 |            950 |            920 |           844 |             838 |         1,008 |         1,081 |         1,064 |         1,155 |         1,089 |           982 |           875 |           630 |           549 | 318 ns | 320 ns |
+|         RunHard |         1,403 |          1,644 |          1,558 |         1,427 |           1,391 |         1,974 |         2,102 |         2,037 |         2,046 |         2,044 |         1,855 |         1,655 |         1,041 |           928 | 586 ns | 582 ns |
+																													   
+
+
+## Allocation, from the 1671st
+
+Bytes allocated per operation, measured in the same run as the 1671st column above. There is
+one column because this is the first version measured for it; later runs add to it the way the
+timings do.
+
+| Method | [1671st](https://github.com/asc-community/AngouriMath/commit/253b5a8d598a9a1d721b777340bd53ae3be12f99) |
+|---|--:|
+| ParseEasy | 18,052 B |
+| ParseHard | 3,486,004 B |
+| SimplifyEasy | 127,578 B |
+| SimplifyHard | 3,710,538,008 B |
+| Derivate | 52,821 B |
+| SolveEasy | 20,213,448 B |
+| SolveEasyMedium | 79,613 B |
+| SolveMedium | 553,368 B |
+| SolveMediumHard | 152,243,208 B |
+| SolveHard | 1,341,716,112 B |
+| EvalEasy | none |
+| EvalTrig | 1,341,378 B |
+| EvalTrigPrecise | 12,743,208 B |
+| CompileEasy | 16,200 B |
+| CompileHard | 37,944 B |
+| RunEasy | none |
+| RunMedium | none |
+| RunHard | none |
+
+**`EvalEasy` allocating nothing is the proof of the caching note above**, rather than a further
+argument for it. Evaluating `1 + 2 + log(2, 3) + sqrt(4) - 4 ^ 7 + e * pi` cannot allocate zero
+bytes; a dictionary lookup can. `RunEasy`, `RunMedium` and `RunHard` allocate nothing for the
+honest reason -- a compiled delegate over `Complex` has nothing to put on the heap.